Effect of assortative mating on genetic change due to selection

Summary Two mathematical models (A and B) were used to study joint effects of selection and assortative mating on genetic change. Computer simulation was used to verify and extend the results. In each model, the genotype was additive with equal effects at each of N loci and the environmental distribution was N(0, ²). In Model A, each locus had two alleles; in Model B, allelic effects at each locus followed a normal distribution. Using Model A, genetic change with assortative or random mating of selected parents was evaluated for combinations of number of loci (N = 1, 2, 3), heritability in base population (H^[0] = 0.2, 0.5, 0.8), allelic frequency in base population (p = 0.1, 0.5), and proportion selected ( = 0.20, 0.85). Using Model B, genetic change with or without assortative mating was calculated for combinations of N (1, 2, 3, 5, 10, 100, H^[0] (0.2, 0.5, 0.8) and (0.20, 0.85). Response to selection under both mating systems in a finite population was estimated using Model A from 200 replications of a computer simulation; this was done for all combinations of N (1,2, 3, 5, 10) and (0.20, 0.85), with H^[0] = 0.5 and p = 0.1. Results obtained with both models indicate that the effect of assortative mating on genetic change increases with H^[0] and , and decreases with p. With Model A, the relationship between N and the effect of assortative mating on genetic change was not clear; with Model B, however, the advantage of assortative over random mating increased with N, as expected. Simulation results were in agreement with theory of Model A. This study indicates that selection with assortative mating can have a sizable (10 to 20%) long-term advantage over selection with random mating of parents when H^[0] is high, p is low and is large.     

QTL analysis of an advanced backcross of Lycopersicon peruvianum to the cultivated tomato and comparisons with QTLs found in other wild species

 A BC₃ population previously developed from a backcross of Lycopersicon peruvianum, a wild relative of tomato, into the cultivated variety L. esculentum was analyzed for QTLs. Approximately 200 BC₄ families were scored for 35 traits in four locations worldwide. One hundred and sixty-six QTLs were detected for 29 of those traits. For more than half of those 29 traits at least 1 QTL was detected for which the presence of the wild allele was associated with an agronomically beneficial effect despite the inferior phenotype of the wild parent. Eight QTLs for fruit weight could be followed through the BC₂, BC₃, and BC₄, generations, supporting the authenticity of these QTLs. Comparisons were made between the QTLs found in this study and those found in studies involving two other wild species; the results showed that while some of these QTLs can be presumed to be allelic, most of the QTLs detected in this study are ones not previously discovered. Received: 9 April 1997 / Accepted: 20 May 1997     

Simultaneous marker-assisted selection for multiple traits in autogamous crops

A method is presented for the selection of parents with the aim of obtaining improved genotypes in the progeny of a cross. The procedure is designed to select in several unrelated traits simultaneously and is based on the selection of molecular markers that are linked to QTLs. The method was compared with conventional phenotypic selection in simulation experiments for a number of genetic structures underlying the traits and several types of parental populations. Although the method in general provides good results, some of the underlying assumptions may be violated quite easily, thereby reducing the applicability of the procedure in practice. Received: 10 September 1999 / Accepted: 24 August 2000     

Marker-assisted selection in autogamous RIL populations: a simulation study

 Molecular markers may enable plant breeders to select indirectly for genes affecting quantitative traits by selecting for molecular markers closely linked to these genes (marker-assisted selection, MAS). We have assessed the effectiveness of MAS compared to phenotypic selection. Key variables in this assessment were: trait heritability, selection intensity, genetic architecture and uncertainty in QTL mapping. Simulation studies showed that the application of MAS in autogamous crops, with the objective of obtaining transgressive genotypes, can improve selection results when compared to conventional selection procedures. Marker-assisted selection appears particularly promising when dominant alleles at quantitative trait loci are present and linked in coupling phase. Uncertainty in estimated QTL map positions reduces the benefits of marker-assisted selection, but this reduction remains limited in most cases. Received: 5 September 1997 / Accepted: 6 October 1997     

Comparison between marker-assisted selection and phenotypical selection in a set of Arabidopsis thaliana recombinant inbred lines

 Parents were selected from a well-characterised Arabidopsis recombinant inbred line (RIL) population based on (1) their phenotype for flowering time or (2) marker and QTL information that had been assessed previously. The F₂ offspring obtained from pairs of selected RILs was analysed for these traits, and the results obtained with these two methods of selection were compared. Selection based on marker and QTL information gave approximately the same result as selection based on phenotype. The relative high heritability of flowering time in Arabidopsis facilitated successful phenotypical selection. The difference in selection result that was anticipated to be in favour of the marker-assisted approach was therefore not observed. Received: 29 November 1997 / Accepted: 8 June 1998     

Rules for assortative mating in relation to selection for linear merit functions

Summary This study examined how assortative mating (without selection) based on linear combinations of two traits could be used to change genetic parameters so as to increase efficiency of selection. The efficiency of the Smith-Hazel index for improvement of multiple traits is a function of phenotypic and genetic variances and covariances, and of the relative economic values of the traits involved. Assortative mating is known to change genetic variances and covariances. Recursive formulae were derived to obtain these variances and covariances after t generations of assortative mating on linear combinations (mating rules) of phenotypic values for two traits, with a given correlation between mates. Selection efficiency after t generations of assortative mating without selection was expressed as a function of random mating genetic parameters, economic values, the mating rule, and the correlation between mates. Selection efficiency was maximized with respect to the coefficients in the mating rule. Because the objective function was nonlinear, a computer routine was used for maximizing it. Two cases were considered. When random mating heritabilities for the two traits were h_X²=0.25 and h_Y²=0.50, the genetic correlation r_XY=-0.60, and the economic values were a_X=3 and a_Y=1, continued assortative mating based on the optimal mating rule for 31 generations (with a correlation of 0.80 between mates) increased selection efficiency by 29%. Heritabilities changed to 0.38 and 0.66, respectively, and the genetic correlation became – 0.79. When h_X²=0.60, h_Y²=0.60, r_XY=– 0.20, a₁=1 and a₂=1, 36 generations of continued assortative mating with the optimal mating rule increased the efficiency of selection by 17%, heritabilities became h_X²= h_Y²=0.71, and the genetic correlation changed to 0.25. Only three generations of assortative mating were required to change the sign of the genetic correlation.     

Effects of genetic architecture on the evolution of assortative mating under frequency-dependent disruptive selection

We consider a model of sympatric speciation due to frequency-dependent competition, in which it was previously assumed that the evolving traits have a very simple genetic architecture. In the present study, we numerically analyze the consequences of relaxing this assumption. First, previous models assumed that assortative mating evolves in infinitesimal steps. Here, we show that the range of parameters for which speciation is possible increases when mutational steps are large. Second, it was assumed that the trait under frequency-dependent selection is determined by a single locus with two alleles and additive effects. As a consequence, the resultant intermediate phenotype is always heterozygous and can never breed true. To relax this assumption, here we add a second locus influencing the trait. We find three new possible evolutionary outcomes: evolution of three reproductively isolated species, a monomorphic equilibrium with only the intermediate phenotype, and a randomly mating population with a steep unimodal distribution of phenotypes. Both extensions of the original model thus increase the likelihood of competitive speciation.     

Sexual size dimorphism and assortative mating for morphological traits in Passer domesticus

In this study, assortative mating for different morphological traits was studied in a captive population of house sparrows (Passer domesticus). Males were larger than females. Assortative mating was found for tail length, wing length and general body size. Males with larger badge size mated with females with longer tails. The strongest assortative mating occurred for tail length (r=0.77), and this assortative mating remained significant after controlling for wing length, mass and tarsus length, suggesting that it was not an artefact of assortative mating for body size. The possibility of sexual selection for tail length in the house sparrow is discussed.     

Assortative mating through a mechanism of sexual selection

We propose that assortative mating can arise through a mechanism of sexual selection by active female choice of partners based on a 'self-seeking like' decision rule. Using a mathematical model, we show that a gene can be selected that make females to choose mates that are similar to themselves with respect to an arbitrary tag, even if two independent and unlinked genes determine the preference and the tag. The necessary requisite for this process to apply is an asymmetry between partners, such that the female can choose the male but this one must always accept to mate. The fitness advantage is due to linkage disequilibrium built up between both genes. Simulations have been run to check the algebraic results and to analyse the influence of several factors on the evolution of the system. Any factor that favors linkage disequilibrium also favors the evolution of the preference allele. Moreover, in a large population subdivided in small subpopulations connected by migration, the assortative mating homogenizes the population genotypic structure for the tags in contrast to random mating that maintains most of the variation.     

Accuracy of mapping quantitative trait loci in autogamous species

Summary The development of linkage maps with large numbers of molecular markers has stimulated the search for methods to map genes involved in quantitative traits (QTLs). A promising method, proposed by Lander and Botstein (1989), employs pairs of neighbouring markers to obtain maximum linkage information about the presence of a QTL within the enclosed chromosomal segment. In this paper the accuracy of this method was investigated by computer simulation. The results show that there is a reasonable probability of detecting QTLs that explain at least 5% of the total variance. For this purpose a minimum population of 200 backcross or F₂ individuals is necessary. Both the number of individuals and the relative size of the genotypic effect of the QTL are important factors determining the mapping precision. On the average, a QTL with 5% or 10% explained variance is mapped on an interval of 40 or 20 centiMorgans, respectively. Of course, QTLs with a larger genotypic effect will be located more precisely. It must be noted, however, that the interval length is rather variable.     

Mapping of one major gene and of QTLs involved in resistance to clubroot in Brassica napus

Clubroot, caused by Plasmodiophora brassicae, is a damaging disease of Brassica napus. Genetic control and mapping of loci involved in high and partial quantitative resistance expressed against two single spore isolates (Pb137–522 and K92–16) were studied in the F₁ and DH progenies of the cross Darmor-bzh (resistant) x Yudal (susceptible). The high level of resistance expressed by Darmor-bzh to isolate Pb137–522 was found to be mainly due to a major gene, which we have named Pb-Bn1, located on linkage group (LG) DY4. Partial quantitative resistance showed by Darmor-bzh to the K92–16 isolate arose from the association of at least two additive QTLs detected on LGs DY4 and DY15; the QTL on DY4, explaining 19% of the variance, was mapped at the same position as the major gene Pb-Bn1. Epistatic interactions between nine regions with or without additive effects were detected. The total phenotypic variation accounted for by additive and epistatic QTLs ranged from 62% to 81% depending on the isolate. For one isolate, the relative effect due to additivity was similar to that due to epistasis. Received: 10 November 1999 / Accepted:18 February 2000     

A general linear model for the genotypic covariance between relatives under assortative mating

A linear model for the genotypic covariance between relatives under assortative mating comprising the classical linear model and the model of selective assortative mating is proposed. The general conditions on the genetical and developmental mechanisms of quantitative characters, as well as on selection and the mating system, on which the model is based, are explicitly stated and discussed. A classification of different relationships is presented and it is shown that these conditions are sufficient to obtain the genotypic covariance between relatives only if the relationship is a combination of descendant-ancestor, full sib, Type 1 and Nth uncle-niece relationships. All the traditional relationships, i.e., those for which the covariances of the relatives have been obtained in the literature, fall into this category. These conditions also ensure that the regression of the individual's genotypic value on the genotypic value or phenotype of any of its ancestors is always linear.Paper No. 6619 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, North Carolina. This investigation was supported in part by NIH Research Grant No. GM 11546 from the National Institute of General Medical Sciences     

Mapping oligogenic resistance to powdery mildew in mungbean with RFLPs

We have used restriction fragment length polymorphisms (RFLPs) to map genes in mungbean (Vigna radiata) that confer partial resistance to the powdery mildew fungus, Erysiphe polygoni. DNA genotypes for 145 RFLP loci spanning 1570 centimorgans of the mungbean genome were assayed in a population of 58 F₂ plants. This population was derived from a cross between a moderately powdery mildew resistant (VC3980A) and a susceptible (TC1966) mungbean parent. F₃ lines derived from the F₂ plants were assayed in the field for powdery mildew response and the results were compared to the RFLP genotype data, thereby identifying loci associated with powdery mildew response. A total of three genomic regions were found to have an effect on powdery mildew response, together explaining 58% of the total variation. At 65 days after planting, two genomic regions were significantly associated with powdery mildew resistance. For both loci, the allele from VC3890A was associated with increased resistance. At 85 days, a third genomic region was also associated with powdery mildew response. For this locus, the allele from the susceptible parent (TC1966) was the one associated with higher levels of powdery mildew resistance. These results indicate that putative partial resistance loci for powdery mildew in mungbean can be identified with DNA markers, even in a population of modest size analyzed at a single location in a single year.     

Assortative mating for a quantitative character

Phenotypic assortative mating is investigated for a character determined by additive loci without dominance and a stochastically independent environment. Conditional-expectation arguments are used to calculate the equilibrium values of the phenotypic variance and the correlation between sundry relatives. For the latter, it suffices to suppose that the regressions of an individual's genotype on his phenotype and of his phenotype on that of his mate are linear. For the former, linearity of the regression of the allelic effects on the phenotype is also posited. The biological implications of these assumptions are discussed.Supported by National Science Foundation Grant DEB81-03530     

A model for marker-assisted selection among single crosses with multiple genetic markers

 Trait means of marker genotypes are often inconsistent across experiments, thereby hindering the use of regression techniques in marker-assisted selection. Best linear unbiased prediction based on trait and marker data (TM-BLUP) does not require prior information on the mean effects associated with specific marker genotypes and, consequently, may be useful in applied breeding programs. The objective of this paper is to present a flanking-marker, TM-BLUP model that is applicable to interpopulation single crosses that characterize maize (Zea mays L.) breeding programs. The performance of a single cross is modeled as the sum of testcross additive and dominance effects at unmarked quantitative trait loci (QTL) and at marked QTL (MQTL). The TM-BLUP model requires information on the recombination frequencies between flanking markers and the MQTL and on MQTL variances. A tabular method is presented for calculating the conditional probability that MQTL alleles in two inbreds are identical by descent given the observed marker genotypes (G ^k _obs) at the kth MQTL. Information on identity by descent of MQTL alleles can then be used to calculate the conditional covariance of MQTL effects between single crosses given G ^k _obs. The inverse of the covariance matrix for dominance effects at unmarked QTL and MQTL can be written directly from the inverse of the covariance matrices of the corresponding testcross additive effects. In practice, the computations required in TM-BLUP may be prohibitive. The computational requirements may be reduced with simplified TM-BLUP models wherein dominance effects at MQTL are excluded, only the single crosses that have been tested are included, or information is pooled across several MQTL. Received: 22 June 1997 / Accepted: 25 February 1998     

Genetic mapping in maize with hybrid progeny across testers and generations: plant height and flowering

DNA markers were used to identify quantitative trait loci (QTLs) for plant height, ear height, and three flowering traits in hybrid progeny of two generations (F_2:3, F_6:8) of lines from a Mo17×H99 maize population. For both generations, testcross (TC) progeny were developed by crossing the lines to three inbred testers (B91, A632, B73). The hybrid progeny from the two generations were evaluated at the same locations but in different years as per an early generation testing program. QTLs were identified within each TC population and for mean testcross (MTC) performance. Overall, more QTLs were detected in the F_6:8 than the F_2:3 generation. Totalled over all five traits, 41 (B91) to 69% (B73) of the QTLs for tester effects and 67% of the QTLs for MTC detected in the F_2:3 generation were verified in the F_6:8 generation. Although differences in relative rank of the QTL effects across generations were observed, especially for the flowering traits, parental contributions were nearly always consistent. Several (8–11) QTLs were identified with effects for all three tester populations and for all traits except the anthesis-silk interval, which had only two such regions. Over all five traits, previous evaluations in this population identified 26 QTLs with consistent effects for two (F_2:3, F_6:8) inbred-progeny evaluations, and 20 (77%) were also associated with MTC in at least one of the generations evaluated herein. In all instances of common inbred and TC QTLs, parental contributions were the same. Received: 26 November 1999 / Accepted: 18 April 2000     

Quantitative trait loci for grain quality, productivity, morphological and agronomical traits in sorghum (Sorghum bicolor L. Moench)

 Quantitative trait loci (QTLs) for grain quality, yield components and other traits were investigated in two Sorghum caudatum×guinea recombinant inbred line (RIL) populations. A total of 16 traits were evaluated (plant height, panicle length, panicle compactness, number of kernels/panicle, thousand-kernel weight, kernel weight/panicle, threshing percentage, dehulling yield, kernel flouriness, kernel friability, kernel hardness, amylose content, protein content, lipid content, germination rate and molds during germination and after harvest) and related to two 113- and 100-point base genetic maps using simple (SIM) and composite (CIM) interval mapping. The number, effects and relative position of QTLs detected in both populations were generally in agreement with the distributions, heritabilities and correlations among traits. Several chromosomal segments markedly affected multiple traits and were suspected of harbouring major genes. The positions of these QTLs are discussed in relation to previously reported studies on sorghum and other grasses. Many QTLs, depending on their relative effects and position, could be used as targets for marker-assisted selection and provide an opportunity for accelerating breeding programmes. Received: 14 February 1998 / Accepted: 4 March 1998